Related papers: Spheroidal harmonics for generalizing the morpholo…
Gravitational features are a fundamental source of information to learn more about the interior structure and composition of planets, moons, asteroids and comets. Gravitational field modeling typically approximates the target body with a…
Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for determining the three-dimensional structures of biological molecules at near-atomic resolution. However, reconstructing helical assemblies presents unique challenges…
We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle…
Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Single particle imaging (SPI) at X-ray free electron lasers (XFELs) is a technique to determine the 3D structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random…
In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
We use SPH simulations to investigate the gravitational fragmentation of expanding shells through the linear and non--linear regimes. The results are analysed using spherical harmonic decomposition to capture the initiation of structure…
This paper introduces a method to preform optical tomography, using 3D radiative transfer as the forward model. We use an iterative approach predicated on the Spherical Harmonics Discrete Ordinates Method (SHDOM) to solve the optimization…
We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
Jeans showed analytically that, in an infinite uniform-density isothermal gas, plane-wave perturbations collapse to dense sheets if their wavelength, $\lambda$, satisfies $\lambda > \lambda_{_{\rm JEANS}} = (\pi a^2 / G \rho_{_0})^{1/2}$…
In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary…
We present a method for speckle holography that is optimised for crowded fields. Its two key features are an iterativ improvement of the instantaneous Point Spread Functions (PSFs) extracted from each speckle frame and the (optional)…
The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property [6]. They are an orthogonal basis of both $L^2(-1,1)$ and the Paley-Wiener space of bandlimited…
Digital image inpainting refers to techniques used to reconstruct a damaged or incomplete image by exploiting available image information. The main goal of this work is to perform the image inpainting process from a set of sparsely…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows…
We analytically investigate the effect of a non-centrosymmetric geometry in the optical second harmonic (SH) generation from a particle made of a centrosymmetric material, in the interior of which quadratic optical processes are suppressed.…